Maths - Functions Of Dual Numbers

On this page we discuss how to extend the scalar functions (that we discussed on this page) to the situation where the domain and/or codomain are double numbers, we also discuss functions like normalise.

As usual, we evaluate the inverse by multiplying top and bottom by the conjugate:

w = (x - ε y)/(x + ε y)(x - ε y)

w = (x - ε y)/(x²)

so the u and v components are:

u = x /(x²)= 1/x
v = -y /(x²)

Evaluating Dual Functions

We can evaluate the value of many dual functions by using infinite series in the same way that we can for scalar functions, we just use the same series that we would use for scalar functions but plug in dual values instead of real values, so if a series exists for real values we can evaluate the dual number function. The higher order powers of ε will be zero so functions of ε are easy to calculate (see exponetial below).

Exponential Function

This is discussed when we discuss polar form and Euler's equation on this page.